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"We are currently on a pace to finish by August the 31st," Mr Biden said in remarks from the White House. "The sooner we can finish, the better."
Since they marched on Kabul on August 14 and 15, the Taliban have been in control of who can approach the perimeter of Hamid Karzai International airport.
They generally have allowed US passport holders through, although some US citizens have been unable to reach the airport and have had to be rescued by US special forces.
"The completion by August 31 is contingent on the Taliban continuing to co-operate," Mr Biden said.
Earlier on Tuesday, Mr Biden met virtually with G7 leaders and Nato Secretary General Jens Stoltenberg. A joint statement from the US and its allies said the Taliban would be held accountable for their actions to prevent terrorism in Afghanistan.
"We will judge them by their actions," Mr Biden said.
Mr Biden touted significant progress in the largest airlift mission in US history, saying the US has flown 70,700 people out of Afghanistan since the Taliban takeover.
He is facing a damaging political backlash over the botched end to America's longest war, and US lawmakers are urging him to slow the rush for the exits.
Mr Biden however said US forces are at increased risk with each passing day, specifically mentioning Afghanistan's ISIS affiliate as being bent on causing deadly mayhem at the airport.
"Every day we're on the ground is another day we know that ISIS-K is seeking to target the airport and attack both US and allied forces and innocent civilians," he said.
"It is a tenuous situation."
US media including Fox News, CNN and the Washington Post, reported on Tuesday that some of the thousands of US troops at Kabul's airport have already started to fly out, with just one week left until the August 31 deadline.
Mr Biden also said he has asked the Pentagon and the State Department for contingency plans to adjust the final evacuation date should it become necessary.
Secretary of State Antony Blinken was due to give a "detailed report" on Wednesday about how many Americans in Afghanistan have left and how many remain, as well as a "projection" of next steps.
Pentagon spokesman John Kirby earlier said the Department of Defence believed it had the ability to remove all Americans who want to leave Afghanistan by August 31.
“We’re absolutely still aiming towards the end of the month,” Mr Kirby said.